Rewrite as a simplified fraction. ${2.28\overline{1} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2281.1111...\\ 100x &= 228.1111...\end{align*}}$ Subtracting the two equations, we have: ${900x = 2053}$ ${x = \dfrac{2053}{900}} \text{or} {2 \dfrac{253}{900}}$